February 2014
Beginner
1248 pages
62h 25m
English
Content preview from Java™ How To Program (Early Objects), Tenth Edition
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19.4.2 Efficiency of the Binary Search
In the worst-case scenario, searching a sorted array of 1023 elements takes only 10 comparisons when using a binary search. Repeatedly dividing 1023 by 2 (because after each comparison we can eliminate half the array) and rounding down (because we also remove the middle element) yields the values 511, 255, 127, 63, 31, 15, 7, 3, 1 and 0. The number 1023 (210 – 1) is divided by 2 only 10 times to get the value 0, which indicates that there are no more elements to test. Dividing by 2 is equivalent to one comparison in the binary search algorithm. Thus, an array of 1,048,575 (220 – 1) elements takes a maximum of 20 comparisons to find the key, and an array of over one billion elements takes a maximum of 30 ...
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